login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A039787 Primes p such that p-1 is squarefree. 16
2, 3, 7, 11, 23, 31, 43, 47, 59, 67, 71, 79, 83, 103, 107, 131, 139, 167, 179, 191, 211, 223, 227, 239, 263, 283, 311, 331, 347, 359, 367, 383, 419, 431, 439, 443, 463, 467, 479, 499, 503, 547, 563, 571, 587, 599, 607, 619, 643, 647, 659, 683, 691, 719, 743 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

An equivalent definition: numbers n such that phi(n) is equal to the squarefree kernel of n-1.

Minimal value of first differences (between odd terms) is 4. Primes p such that both p and p + 4 are terms are: 3, 7, 43, 67, 79, 103, 223, 439, 463, 499, 643, 823, ... - Zak Seidov, Apr 16 2013

The density of this set in A000040 is Artin's constant A = A005596 = 37.39...%, see Mirsky. - Charles R Greathouse IV, Oct 26 2015

LINKS

N. J. A. Sloane, Table of n, a(n) for n = 1..25000, Oct 25 2015 (extending earlier b-file of Zak Seidov)

Theodor Estermann, Einige Sätze über quadratfreie Zahlen, Math. Ann. 105:1 (1931), pp. 653-662.

Leon Mirsky, The number of representations of an integer as the sum of a prime and a k-free integer, American Mathematial Monthly 56:1 (1949), pp. 17-19.

EXAMPLE

phi(43)=42, 42=2^1*3^1*7^1, 2*3*7=42.

p=223 is here because p-1=222=2*3*37

MAPLE

isA039787 := proc(n)

    if isprime(n) then

        numtheory[issqrfree](n-1) ;

    else

        false;

    end if;

end proc:

for n from 2 to 100 do

    if isA039787(n) then

        printf("%d, ", n) ;

    end if;

end do: # R. J. Mathar, Apr 17 2013

with(numtheory): lis:=[]; for n from 1 to 10000 do if issqrfree(ithprime(n)-1) then lis:=[op(lis), ithprime(n)]; fi; od: lis; # N. J. A. Sloane, Oct 25 2015

MATHEMATICA

Select[Prime[Range[132]], SquareFreeQ[#-1]&](* Zak Seidov, Aug 22 2012 *)

PROG

(MAGMA) [p: p in PrimesUpTo(780) | IsSquarefree(p-1)];  // Bruno Berselli, Mar 03 2011

(PARI) is(n)=isprime(n) && issquarefree(n-1) \\ Charles R Greathouse IV, Jul 02 2013

(PARI) forprime(p=2, 1e3, if(issquarefree(p-1), print1(p", "))); \\ Altug Alkan, Oct 26 2015

CROSSREFS

Cf. A000010, A007947, A049092 (complement).

Sequence in context: A165318 A108184 A049091 * A267503 A226937 A227199

Adjacent sequences:  A039784 A039785 A039786 * A039788 A039789 A039790

KEYWORD

nonn

AUTHOR

Olivier Gérard

EXTENSIONS

More terms from Labos Elemer

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 10 23:13 EST 2016. Contains 279021 sequences.